Definition:Ordered Semigroup Automorphism

Definition

Let $\struct {S, \circ, \preceq}$ be an ordered semigroup.

An ordered semigroup automorphism from $\struct {S, \circ, \preceq}$ to itself is a mapping $\phi: S \to S$ that is both:

$(1): \quad$ A semigroup automorphism, that is, a semigroup isomorphism from the semigroup $\struct {S, \circ}$ to itself

$(2): \quad$ An order isomorphism from the ordered set $\struct {S, \preceq}$ to itself.

Also see

• Definition:Ordered Structure Automorphism

Linguistic Note

The word automorphism derives from the Greek morphe (μορφή) meaning form or structure, with the prefix iso- meaning equal.

Thus automorphism means self structure.

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {III}$: The Natural Numbers: $\S 15$: Ordered Semigroups